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MATH / When working modulo m, the notation a^(−1) is used to denote the residue b for which abequiv 1pmod{m}, if any exists. For how many integers a satisfying 0≤a<100 is it true that …

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problem

When working modulo mm, the notation a−1a^{-1} is used to denote the residue bb for which $ab\equiv 1\pmod{m}$, if any exists. For how many integers aa satisfying 0≤a<1000 \le a < 100 is it true that $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$?
Plain-text mathematical notation (without MathML)
When working modulo m, the notation a^(−1) is used to denote the residue b for which $ab\equiv 1\pmod{m}$, if any exists. For how many integers a satisfying 0≤a<100 is it true that $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$?
Original LaTeX notation
When working modulo $m$, the notation $a^{-1}$ is used to denote the residue $b$ for which $ab\equiv 1\pmod{m}$, if any exists. For how many integers $a$ satisfying $0 \le a < 100$ is it true that $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$?

level

Level 5

type

Number Theory

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Source and history

task_id
84e3b233-2e90-558b-b32e-732e439023d4
task_key
number~5ftheory--test--84e3b233-2e90-558b-b32e-732e439023d4
task_revision_id
1
config / split
number_theory / test

Official source

initial import